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Single-variable equations

# Does x satisfy the equation?

Finding all the values of the variable x that make the left-hand-side of an equation equal the right-hand-side is called solving the equation for x. When we set out to find these values, x is called the unknown. Once we have found the values they are called the solutions or roots of the equation. We say that they make the equation true. We also say that these values of x satisfy the equation.

Is w=21 a solution of the equation $7=\frac{w}{3}$?

A number is a solution to an equation if plugging it in results in a true statement.

Plug w=21 into the equation and simplify.

 $7=\frac{w}{3}$ $7\;\stackrel{?}{=}\;\frac{21}{3}$ Plug in w=21 $7\;\stackrel{?}{=}\;7$ Divide

Yes, 7=7.
So, w=21 is a solution to the equation
$7=\frac{w}{3}$.

Is m=1 a solution of the equation m-3=7?

A number is a solution to an equation if plugging it in results in a true statement.

Plug m=1 into the equation and simplify.

 m-3=7 $1-3\;\stackrel{?}{=}\;7$ Plug in m=1 $-2\neq\;7$ Add

$-2\neq\;7$, so, m=1 is not a solution to the equation m-3=7.